平成29年度秋期 ITパスポート試験問98

This question's explanation and your answers so far.

問98

頻出度★★☆

次のベン図の網掛けした部分の検索条件はどれか。

出典　平成29年度秋期 ITパスポート試験問98

解説

問 98

Incorrectア
(not A) and (B and C) represents the region that does not belong to A and belongs to both B and C, that is, only the part of the B∩C overlap with A removed. Since the shaded area also includes the B-only and C-only parts, this condition is too narrow and does not match the figure.
イ
正解 The correct answer is イ, (not A) and (B or C). In the Venn diagram, circle A is at the top, circle B at the lower right, and circle C at the lower left, and the three circles overlap. The shaded part covers only the region inside circles B and C that is not contained in circle A (the B-only part, the C-only part, and the lower part where B and C overlap); every part overlapping with A is left white. In other words, it is the region that satisfies both conditions: belonging to at least one of B or C (B or C), and not belonging to A (not A). Therefore (not A) and (B or C) matches it.
Incorrectウ
(not A) or (B and C) is the union of all regions not belonging to A and the region B∩C. Because not A even includes the white background outside the three circles, it does not match the figure, in which the shading is confined to the interior of the circles (the range is too wide).
Incorrectエ
(not A) or (B or C) is the region formed by combining everything outside A and everything belonging to at least one of B or C. It covers almost the entire area except the part that is inside A and belongs to neither B nor C. This far exceeds the shaded range, so it is wrong.

ここがポイント

Correspondence between a three-circle Venn diagram and logical operations: AND is the intersection (the overlap belonging to both), OR is the union (the combination belonging to at least one), and NOT is the complement (the outside of that set).
Steps to put the shaded part into words: first use B or C to combine B and C into one range, then use not A to remove the part overlapping with A. Joining these two conditions with and matches how the figure is shaded.

用語

解答問98イ